| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2022 |
| Session | June |
| Marks | 5 |
| Topic | Composite & Inverse Functions |
| Type | Verify composite identity |
| Difficulty | Moderate -0.3 Part (a) is trivial identification of where denominator equals zero. Part (b) requires computing f(f(x)) and showing it equals x, which is algebraically straightforward but involves careful fraction manipulation. Part (c) follows immediately from the self-inverse property. This is a standard functions question requiring routine algebraic skills with no novel insight, making it slightly easier than average. |
| Spec | 1.02v Inverse and composite functions: graphs and conditions for existence |
The function $f$ is defined by
$$f(x) = \frac{5x}{7x - 5}$$
\begin{enumerate}[label=(\alph*)]
\item The domain of $f$ is the set $\{x \in \mathbb{R} : x \neq a\}$
State the value of $a$ [1 mark]
\item Prove that $f$ is a self-inverse function [3 marks]
\item Find the range of $f$ [1 mark]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2022 Q4 [5]}}